Bilinear form, Pfaffian, soliton and breather solutions for a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics

Bilinear form, Pfaffian, soliton and breather solutions for a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Bilinear form, Pfaffian, soliton and breather solutions for a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics Chong-Dong Cheng, Bo Tian, Yuan Shen, Tian-Yu Zhou This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2201350/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 09 Jan, 2023 Read the published version in Nonlinear Dynamics → Version 1 posted 5 You are reading this latest preprint version Abstract In this paper, a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics is studied. Bilinear form under certain constraints is given via the Hirota method. The Nth-order Pfaffian solutions are proved via the Pfaffian technique, where N is a positive integer. N-soliton and the higher-order breather solutions are derived from the Nth-order Pfaffian solutions. Y/X-type solitons are constructed via adding some conditions to the N-soliton solutions. Elastic and inelastic interactions between the two solitons are presented graphically. Y/X-type breathers are constructed via adding some conditions to the higher-order breather solutions. Y-type breathers describe the inelastic interactions between the two breathers, and the X-type breathers describe the different two-breather structure. We investigate the influence of the coefficients in the system on those solitons and breathers as follows: the amplitudes of those solitons and breathers are related to l1 and l2; the periods of those breathers are related to l1, l2, l3 and l5, where l1, l2, l3 and l5 are the constant coefficients in the system. Fluid mechanics Plasma physics (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system Pfaffian solutions Soliton solutions Breather solutions Full Text Cite Share Download PDF Status: Published Journal Publication published 09 Jan, 2023 Read the published version in Nonlinear Dynamics → Version 1 posted Editorial decision: Major revisions 16 Nov, 2022 Reviewers agreed at journal 13 Nov, 2022 Reviewers invited by journal 13 Nov, 2022 Editor assigned by journal 26 Oct, 2022 First submitted to journal 25 Oct, 2022 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2201350","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":151675019,"identity":"c7ee50cb-f086-41c0-817a-f4b6fa9ee013","order_by":0,"name":"Chong-Dong Cheng","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA4UlEQVRIiWNgGAWjYDACCRDBBsTsPVCRA0Rr4TkDJBJI0iKRQ6QW/tnNxx5+KbPJk498e0y68AeDHN+NBMbPBfgsuXMs3VjmXFqx4e28NOkZCQzGkjcSmKVn4NFiIJFjJi3Zdjhx42wggyeBIXHDjQQ2Zh6itMw8A9ZST5QWyY9ALfMleMBaEgwIaZG4kZYmzXAuLXEDT16y9Yw0CcOZZx42S+PTwj8j+ZjkjzKbxPntZw/eLrCxkec7nnzwMz4tIAB2hsEBIAMSTYwNBDQAlfwAEvINYC2jYBSMglEwCjABAN+9SL1vYIhtAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-1958-2878","institution":"Beijing University of Posts and Telecommunications","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Chong-Dong","middleName":"","lastName":"Cheng","suffix":""},{"id":151675020,"identity":"432f9abe-268e-49ed-84b9-b4170192fe90","order_by":1,"name":"Bo Tian","email":"","orcid":"","institution":"Beijing University of Posts and Telecommunications","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Bo","middleName":"","lastName":"Tian","suffix":""},{"id":151675021,"identity":"7e96c20a-2b48-4fe4-b67b-303c203965ed","order_by":2,"name":"Yuan Shen","email":"","orcid":"","institution":"Beijing University of Posts and Telecommunications","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Yuan","middleName":"","lastName":"Shen","suffix":""},{"id":151675022,"identity":"8bfbbe31-37e4-49d8-a6d8-b764632565ea","order_by":3,"name":"Tian-Yu Zhou","email":"","orcid":"","institution":"Beijing University of Posts and Telecommunications","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Tian-Yu","middleName":"","lastName":"Zhou","suffix":""}],"badges":[],"createdAt":"2022-10-25 08:16:26","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2201350/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2201350/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s11071-022-08189-6","type":"published","date":"2023-01-09T18:19:11+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":44716797,"identity":"368cffa3-d8e2-410b-909b-171d820deac5","added_by":"auto","created_at":"2023-10-16 18:30:42","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2423161,"visible":true,"origin":"","legend":"","description":"","filename":"Manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2201350/v1_covered_9300d81e-ac18-43be-a78b-799a268b2fde.pdf"}],"financialInterests":"","formattedTitle":"Bilinear form, Pfaffian, soliton and breather solutions for a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":true,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"nonlinear-dynamics","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"nody","sideBox":"Learn more about [Nonlinear Dynamics](https://www.springer.com/journal/11071)","snPcode":"11071","submissionUrl":"https://submission.nature.com/new-submission/11071/3","title":"Nonlinear Dynamics","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false},"keywords":"Fluid mechanics, Plasma physics, (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system, Pfaffian solutions, Soliton solutions, Breather solutions","lastPublishedDoi":"10.21203/rs.3.rs-2201350/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2201350/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"In this paper, a (2+1)-dimensional generalized Konopelchenko-Dubrovsky-Kaup-Kupershmidt system in fluid mechanics and plasma physics is studied. 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